Q: What are the factor combinations of the number 41,534,017?

 A:
Positive:   1 x 415340177 x 593343131 x 133980737 x 112254149 x 847633217 x 191401259 x 160363739 x 562031147 x 362111519 x 273431813 x 229095173 x 8029
Negative: -1 x -41534017-7 x -5933431-31 x -1339807-37 x -1122541-49 x -847633-217 x -191401-259 x -160363-739 x -56203-1147 x -36211-1519 x -27343-1813 x -22909-5173 x -8029


How do I find the factor combinations of the number 41,534,017?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 41,534,017, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 41,534,017
-1 -41,534,017

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 41,534,017.

Example:
1 x 41,534,017 = 41,534,017
and
-1 x -41,534,017 = 41,534,017
Notice both answers equal 41,534,017

With that explanation out of the way, let's continue. Next, we take the number 41,534,017 and divide it by 2:

41,534,017 ÷ 2 = 20,767,008.5

If the quotient is a whole number, then 2 and 20,767,008.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 41,534,017
-1 -41,534,017

Now, we try dividing 41,534,017 by 3:

41,534,017 ÷ 3 = 13,844,672.3333

If the quotient is a whole number, then 3 and 13,844,672.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 41,534,017
-1 -41,534,017

Let's try dividing by 4:

41,534,017 ÷ 4 = 10,383,504.25

If the quotient is a whole number, then 4 and 10,383,504.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 41,534,017
-1 41,534,017
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

173137492172597391,1471,5191,8135,1738,02922,90927,34336,21156,203160,363191,401847,6331,122,5411,339,8075,933,43141,534,017
-1-7-31-37-49-217-259-739-1,147-1,519-1,813-5,173-8,029-22,909-27,343-36,211-56,203-160,363-191,401-847,633-1,122,541-1,339,807-5,933,431-41,534,017

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